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Ellipse question

2016 · Shift 2 · Q29

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PYQ Library
JEE Advanced
Mathematics
Ellipse
2016 · Shift 2 · Q29

Ellipse question

2016 · Shift 2 · Q29

JEE AdvancedMathematicsEllipseMCQ+3 / −1

Let

{F_1}\left( {{x_1},0} \right)

and

{F_2}\left( {{x_2},0} \right)

for

{{x_1} \lt 0}

and

{{x_2} \gt 0}

, be the foci of the ellipse

{{{x^2}} \over 9} + {{{y^2}} \over 8} = 1

. Suppose a parabola having vertex at the origin and focus at

{F_2}

intersects the ellipse at point

M

in the first quadrant and at point

N

in the fourth quadrant. The orthocentre of the triangle

{F_1}MN

is

A
$\left( { - {9 \over {10}},0} \right)$
B
$\left( { {2 \over {3}},0} \right)$
C
$\left( { {9 \over {10}},0} \right)$
D
$\left( {{2 \over 3},\sqrt 6 } \right)$

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